K-Theory Tools For Local and Asymptotic Cyclic Cohomology

Abstract

A generalization of Connes-Thom isomorphism is given for stable, homotopy invariant, and split exact functors on separable $C^{\ast }$-algebras. As examples of these functors, we concentrate on asymptotic and local cyclic cohomology and the result is applied to improve some formulas in asymptotic and local cyclic cohomology of $C^{\ast }$-algebras. As an other application, it is shown that these cyclic theories are rigid after Rieffel's deformation quantizations.

12pages